Question

For what value of $k$, will the given equations in two variables represent coincident lines $2x+32y+3=0$ and $3x+48y+k=0?$

• A. $\frac{2}{3}$
• B. $\frac{3}{2}$
• C. $\frac{9}{2}$
• D. $1$

Answer 1

The correct option is C $\frac{9}{2}$

We write the equations in the form $ax+by+c=0,$

The lines will be coincident if :

$\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$

Here $a_1=2,a_2=3,b_1=32,b_2=48,c_1=3,c_2=k$

$\frac{a_1}{a_2}=\frac{2}{3},\frac{b_1}{b_2}=\frac{32}{48}=\frac{2}{3},\frac{c_1}{c_2}=\frac{3}{k}.\therefore \frac{3}{k}=\frac{2}{3}⟹k=\frac{9}{2}$